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Who is White House chief of staff John Kelly?

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The President is miffed by the constraints Kelly has placed

John Bolton is one person who can no longer see the President

Washington (CNN)President Donald Trump is torn.

As he enters a month potted with legislative hurdles and governing challenges, he finds himself split between countervailing instincts: while he's grown increasingly irritated by the restrictions placed by new chief of staff John Kelly on his communications, he's come to recognize that achieving his goals in Washington will require changes in the way his White House is run.

The President is miffed by the constraints Kelly has placed on his access to staffers and outside associates, administration officials tell CNN.

Though the Oval Office once was abuzz with visitors who dropped by unannounced, those who want to speak to the President now must go through Kelly first, and Trump has privately complained that he has found out people tried to reach him only to be denied by Kelly.

John Bolton is one person who can no longer see the President. The former ambassador to the United Nations blamed "staff changes" for this as he outlined his plan to exit the Iran nuclear deal in an op-ed published in National Review. He said he wrote the piece because he couldn't reach Trump directly.

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"Although he was once kind enough to tell me 'come in and see me any time,' those days are now over," Bolton wrote.

Since he officially replaced Reince Priebus in late July, Kelly began screening all of the President's incoming calls on the White House switchboard. Kelly makes the ultimate decision of whether that person should talk to the President, and either patches them through or declines their request, according to an administration official.

According to some people outside the White House, Trump has even stopped calling them from his cell phone -- and started calling them from the switchboard.

But there are still those external allies who have Trump's personal number and continue to call him on it -- outside of Kelly's careful watch. However, those who don't have his number must go through the switchboard -- and Kelly -- and have had a much a more difficult time.

To contact the President, "there used to be multiple lanes," one staffer said. "Now there's only one lane."

Trump has resisted some of his new top aide's order, continuing to take calls from the long roster of outside advisers and friends that helped sustain him during the tumultuous first half-year of his presidency. He continues to fume about investigations into Russia's election meddling and perceived disloyalty from fellow Republicans. And he hasn't stopped tweeting angrily about people he sees as enemies, including on Friday lashing out against fired FBI director James Comey.

At the same time, however, Trump has agreed to a more intensive pace of travel, set by Kelly, to sell agenda items that until now have been rolled out haphazardly and without direct buy-in from the commander in chief himself. He'll make a pitch on energy next week in North Dakota, after stopping in Missouri on Wednesday to launch a tax reform push. A West Wing that was once a roiling snake-pit of competing agendas does, for now, appears to be stabilizing.

The dueling inclinations have left the President disgruntled, say people who have spoken to him. As summer ends and Congress returns with a full slate, the direction Trump chooses will assume new levels of consequence, with the nation's finances and his own agenda on the line.

Next week, Trump will press lawmakers to approve billions in emergency funding for victims of Hurricane Harvey. By the end of the month, he'll need to push through measures that avoid a government shutdown and a default on the nation's debt. Through it all, he's pushing a tax reform effort and continues to insist that Obamacare be repealed and replaced.

Also those efforts will require a regimented push, not only from Trump's aides but from Trump himself.

The President maintained in a tweet on Friday that Kelly "is doing a great job" and he "could not be happier."

A senior administration official said that Trump has said similar things behind closed doors, offering praise for his chief of staff's businesslike attitude toward corralling the resources of the federal government behind the recovery efforts in Texas after Hurricane Harvey.

But if Trump is pleased at Kelly's efforts on policy, he's less thrilled at the methods that Kelly is employing to achieve his goals.

A pair of memos distributed on last Monday spelled out a rigid system for providing information to the President and for formalizing decisions that come from the Oval Office, according to people familiar with the documents. It was a change meant to curtail what was previously a haphazard flow of documents or print-outs -- some of dubious origin -- to the stack of reading material that Trump sifts through daily.

Trump has vented frustrations over his lack of access to those who are close to him. As a private businessman, presidential candidate, and new president, Trump grew accustomed to consulting a wide orbit of friends and advisers in late-night phone calls.

On Friday, CNN learned that one of his longest-serving and closest aides, Keith Schiller, has told people he plans to leave his post. The departure would amount to a blow for Trump, who has cherished the familiarity of having a longtime aide steps from the Oval Office.

According to one White House staffer, there has been some grumbling among longtime Trump confidants that they have had a difficult time reaching him -- even through official channels -- since Kelly became chief of staff.

It's not just those outside of the administration who have trouble reaching Trump. Because calling through the switchboard is so tightly monitored, it discourages some White House staffers from using that method to get in touch with the president directly. Instead, they've begun requesting meetings through Kelly -- requests that aren't always granted, an administration official told CNN.